Modeling of the behavior of the electrical power network is of increasing importance in order to ensure reliable electrical service. The electrical power network consists of many interconnected elements, including power generation nodes, transmission systems, distribution systems and loads. Electrical power generators and distribution entities cooperate to achieve delivery of power upon demand. For example, electrical power generation and distribution entities may cooperate to facilitate to transmission of power from Arizona to a high need area in New York City at certain times of day or year, and to facilitate transmission of power from New York state to Arizona at other times of day or year.
In general, the electrical power network can be divided into two main elements, transmission systems and distribution systems. Transmission systems include transmission lines that deliver energy from power generating devices to power substations. Distribution systems are networks that distribute power from the power substations to the individual end-user loads. Distribution systems may also transfer power among themselves.
Transmission systems employ very high voltages, typically on the order of 110 kV to 500 kV AC, and have an interstate extent. Transmission systems transmit power in three phases, and tend to have balanced loads on all three phases. By contrast, distribution systems tend to employ lower distribution voltages (under 66 kV), and typically cover a confined geographical service such as a metropolitan area and its surrounds. While distribution systems are also three phase systems, the loads in distribution systems can be unbalanced due to the presence of two phase and single phase lines and distribution transformers.
Real-time modeling of transmission systems has been used to assist in the efficient allocation of power between power generators and the distribution substations. Real-time models may be generated multiple times per day to determine whether a reallocation in power is required. In the modeling of transmission systems, the distribution systems (i.e. represented by power substations and connected loads) are treated as balanced loads, and thus have composite electrical characteristics that are relatively easy to represent. Moreover, real-time power usage information at the subsystem level is readily available.
Modeling has also been used in distribution systems. However, for several reasons, modeling in distribution systems has typically been limited to non-real time or offline modeling. In particular, unlike transmission systems, real-time power flow measurements at individual loads are not readily available in distribution systems. While the usage of power at individual loads is typically metered (i.e. using electricity meters), the metered power information is typically not available in real time. More specifically, power measurement information from customer electricity meters is usually only retrieved at long intervals, for example, monthly. The lack of real-time power measurement information for the individual loads significantly complicates the development of real-time power flows in distribution systems.
Offline power flows, by contrast, do not require real-time measurement information. Instead, offline power flows employ assumptions about individual loads that suit the problem being addressed. For example, one offline power flow technique assumes full loading of all elements of the distribution network. Such a power flow may be used to identify areas of the distribution network in which increased capacity may be required to ensure proper operation during peak loading times.
Offline power flows, however, have limited usefulness in determining real time resource allocation. Resource allocation in distribution systems is dynamic, and is preferably updated several times per day. Thus, if power flow information is to be used in dynamic resource allocation, then power flows that use real-time power measurements are more desirable than offline power flows.
To satisfy this need, techniques have been developed that generate a real-time power flow in a distribution system using the limited real time power measurements that are available. Such techniques use historical usage information regarding individual loads of a distribution network to estimate power usage based on available real-time power consumption information. For example, real-time power consumption information may be available at different locations on feeder lines, which at least provides some detail as to the power consumption of the distribution system. The historical consumption statistics of various loads connected to the feeders is then used to extrapolate out the measured power consumption to each of the various loads.
For example, consider a situation in which there are three loads on a feeder line, and that real-time measurement information is available for the feeder line. Also consider that two of the loads have roughly the same historical energy consumption record, and that the other load has twice the energy consumption of each of the first two loads. In such a case, the real-time measured energy of the feeder may be allocated at a ratio of 1:1:2. For example, if the real-time measured power on the feeder is 12 kW, it can be assumed that the first two loads are each consuming 3 kW and the third load is consuming 6 kW. This method of allocation in determining real-time power flow is known as scaling.
Thus, through the use of scaling and other techniques known in the art, it is possible to estimate a real-time power flow (details of power usage at each load) for a distribution network having limited real-time power consumption measurement data. Examples of techniques for developing distribution system power flow in this manner are provided in I. Roytelman, S. M. Shahidehpour “State Estimation for Electric Power Distribution Systems in Quasi Real-Time Conditions”, IEEE Trans. On Power Delivery, Vol. 8, No. 4, 1993, pp. 2009–2015; and M. E. Baran, A. W. Kelley “A Branch-Current Based State Estimation Method for Distribution Systems”, IEEE Trans. On Power Systems, Vol. 10, No.1, 1995, pp.483–489, both of which are incorporated herein by reference.
However, there are several impediments to achieving an accurate power flow of a distribution system. Such impediments arise from difficulties in modeling certain types of transformers using standard power flow calculation techniques. For example, one common step in developing a standard power flow is to solve Kirchoff's law equations in matrix format: [I]=[Y][V]. One of the elements of the matrix equation is the admittance matrix [Y], where admittance is the inverse of impedance. During the power flow solution, the inverse of the admittance matrix must be taken. Under typical power flow circumstances, such an operation presents no great difficulty.
However, there exists a certain class of distribution transformers that raise issues with respect to the matrix equation solution. In particular, certain types of transformers connected in a delta configuration have windings that are not referenced to ground. When such “floating” transformer windings are factored into the matrix equations used to solve the power flow, they can generate a divide by zero error, which does not lead to a power flow solution. Thus, such floating transformer windings present a very real impediment to calculating real time power flow for a distribution system.
In addition, delta connected transformers also raise issues in the application of scaling procedures. In particular, the scaling procedures used to allocate measured composite power consumption to individual loads can break down for loads connected to delta connected transformers. Delta connected transformers introduce phase to phase currents which cannot be scaled using normal techniques.
As a consequence, there remains a need for real-time power flow in electrical distribution systems that overcomes problems presented by ungrounded or floating transformer windings and/or phase to phase loading.